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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DEBCHVXX( THRESH, PATH ) 00002 IMPLICIT NONE 00003 * .. Scalar Arguments .. 00004 DOUBLE PRECISION THRESH 00005 CHARACTER*3 PATH 00006 * 00007 * Purpose 00008 * ====== 00009 * 00010 * DEBCHVXX will run D**SVXX on a series of Hilbert matrices and then 00011 * compare the error bounds returned by D**SVXX to see if the returned 00012 * answer indeed falls within those bounds. 00013 * 00014 * Eight test ratios will be computed. The tests will pass if they are .LT. 00015 * THRESH. There are two cases that are determined by 1 / (SQRT( N ) * EPS). 00016 * If that value is .LE. to the component wise reciprocal condition number, 00017 * it uses the guaranteed case, other wise it uses the unguaranteed case. 00018 * 00019 * Test ratios: 00020 * Let Xc be X_computed and Xt be X_truth. 00021 * The norm used is the infinity norm. 00022 00023 * Let A be the guaranteed case and B be the unguaranteed case. 00024 * 00025 * 1. Normwise guaranteed forward error bound. 00026 * A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and 00027 * ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS. 00028 * If these conditions are met, the test ratio is set to be 00029 * ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00030 * B: For this case, CGESVXX should just return 1. If it is less than 00031 * one, treat it the same as in 1A. Otherwise it fails. (Set test 00032 * ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?) 00033 * 00034 * 2. Componentwise guaranteed forward error bound. 00035 * A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i ) 00036 * for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS. 00037 * If these conditions are met, the test ratio is set to be 00038 * ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10). Otherwise it is 1/EPS. 00039 * B: Same as normwise test ratio. 00040 * 00041 * 3. Backwards error. 00042 * A: The test ratio is set to BERR/EPS. 00043 * B: Same test ratio. 00044 * 00045 * 4. Reciprocal condition number. 00046 * A: A condition number is computed with Xt and compared with the one 00047 * returned from CGESVXX. Let RCONDc be the RCOND returned by D**SVXX 00048 * and RCONDt be the RCOND from the truth value. Test ratio is set to 00049 * MAX(RCONDc/RCONDt, RCONDt/RCONDc). 00050 * B: Test ratio is set to 1 / (EPS * RCONDc). 00051 * 00052 * 5. Reciprocal normwise condition number. 00053 * A: The test ratio is set to 00054 * MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )). 00055 * B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )). 00056 * 00057 * 6. Reciprocal componentwise condition number. 00058 * A: Test ratio is set to 00059 * MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )). 00060 * B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )). 00061 * 00062 * .. Parameters .. 00063 * NMAX is determined by the largest number in the inverse of the hilbert 00064 * matrix. Precision is exhausted when the largest entry in it is greater 00065 * than 2 to the power of the number of bits in the fraction of the data 00066 * type used plus one, which is 24 for single precision. 00067 * NMAX should be 6 for single and 11 for double. 00068 00069 INTEGER NMAX, NPARAMS, NERRBND, NTESTS, KL, KU 00070 PARAMETER (NMAX = 10, NPARAMS = 2, NERRBND = 3, 00071 $ NTESTS = 6) 00072 00073 * .. Local Scalars .. 00074 INTEGER N, NRHS, INFO, I ,J, k, NFAIL, LDA, 00075 $ N_AUX_TESTS, LDAB, LDAFB 00076 CHARACTER FACT, TRANS, UPLO, EQUED 00077 CHARACTER*2 C2 00078 CHARACTER(3) NGUAR, CGUAR 00079 LOGICAL printed_guide 00080 DOUBLE PRECISION NCOND, CCOND, M, NORMDIF, NORMT, RCOND, 00081 $ RNORM, RINORM, SUMR, SUMRI, EPS, 00082 $ BERR(NMAX), RPVGRW, ORCOND, 00083 $ CWISE_ERR, NWISE_ERR, CWISE_BND, NWISE_BND, 00084 $ CWISE_RCOND, NWISE_RCOND, 00085 $ CONDTHRESH, ERRTHRESH 00086 00087 * .. Local Arrays .. 00088 DOUBLE PRECISION TSTRAT(NTESTS), RINV(NMAX), PARAMS(NPARAMS), 00089 $ S(NMAX),R(NMAX),C(NMAX), DIFF(NMAX, NMAX), 00090 $ ERRBND_N(NMAX*3), ERRBND_C(NMAX*3), 00091 $ A(NMAX,NMAX),INVHILB(NMAX,NMAX),X(NMAX,NMAX), 00092 $ AB( (NMAX-1)+(NMAX-1)+1, NMAX ), 00093 $ ABCOPY( (NMAX-1)+(NMAX-1)+1, NMAX ), 00094 $ AFB( 2*(NMAX-1)+(NMAX-1)+1, NMAX ), 00095 $ WORK(NMAX*3*5), AF(NMAX, NMAX),B(NMAX, NMAX), 00096 $ ACOPY(NMAX, NMAX) 00097 INTEGER IPIV(NMAX), IWORK(3*NMAX) 00098 00099 * .. External Functions .. 00100 DOUBLE PRECISION DLAMCH 00101 00102 * .. External Subroutines .. 00103 EXTERNAL DLAHILB, DGESVXX, DPOSVXX, DSYSVXX, 00104 $ DGBSVXX, DLACPY, LSAMEN 00105 LOGICAL LSAMEN 00106 00107 * .. Intrinsic Functions .. 00108 INTRINSIC SQRT, MAX, ABS, DBLE 00109 00110 * .. Parameters .. 00111 INTEGER NWISE_I, CWISE_I 00112 PARAMETER (NWISE_I = 1, CWISE_I = 1) 00113 INTEGER BND_I, COND_I 00114 PARAMETER (BND_I = 2, COND_I = 3) 00115 00116 * Create the loop to test out the Hilbert matrices 00117 00118 FACT = 'E' 00119 UPLO = 'U' 00120 TRANS = 'N' 00121 EQUED = 'N' 00122 EPS = DLAMCH('Epsilon') 00123 NFAIL = 0 00124 N_AUX_TESTS = 0 00125 LDA = NMAX 00126 LDAB = (NMAX-1)+(NMAX-1)+1 00127 LDAFB = 2*(NMAX-1)+(NMAX-1)+1 00128 C2 = PATH( 2: 3 ) 00129 00130 * Main loop to test the different Hilbert Matrices. 00131 00132 printed_guide = .false. 00133 00134 DO N = 1 , NMAX 00135 PARAMS(1) = -1 00136 PARAMS(2) = -1 00137 00138 KL = N-1 00139 KU = N-1 00140 NRHS = n 00141 M = MAX(SQRT(DBLE(N)), 10.0D+0) 00142 00143 * Generate the Hilbert matrix, its inverse, and the 00144 * right hand side, all scaled by the LCM(1,..,2N-1). 00145 CALL DLAHILB(N, N, A, LDA, INVHILB, LDA, B, LDA, WORK, INFO) 00146 00147 * Copy A into ACOPY. 00148 CALL DLACPY('ALL', N, N, A, NMAX, ACOPY, NMAX) 00149 00150 * Store A in band format for GB tests 00151 DO J = 1, N 00152 DO I = 1, KL+KU+1 00153 AB( I, J ) = 0.0D+0 00154 END DO 00155 END DO 00156 DO J = 1, N 00157 DO I = MAX( 1, J-KU ), MIN( N, J+KL ) 00158 AB( KU+1+I-J, J ) = A( I, J ) 00159 END DO 00160 END DO 00161 00162 * Copy AB into ABCOPY. 00163 DO J = 1, N 00164 DO I = 1, KL+KU+1 00165 ABCOPY( I, J ) = 0.0D+0 00166 END DO 00167 END DO 00168 CALL DLACPY('ALL', KL+KU+1, N, AB, LDAB, ABCOPY, LDAB) 00169 00170 * Call D**SVXX with default PARAMS and N_ERR_BND = 3. 00171 IF ( LSAMEN( 2, C2, 'SY' ) ) THEN 00172 CALL DSYSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00173 $ IPIV, EQUED, S, B, LDA, X, LDA, ORCOND, 00174 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00175 $ PARAMS, WORK, IWORK, INFO) 00176 ELSE IF ( LSAMEN( 2, C2, 'PO' ) ) THEN 00177 CALL DPOSVXX(FACT, UPLO, N, NRHS, ACOPY, LDA, AF, LDA, 00178 $ EQUED, S, B, LDA, X, LDA, ORCOND, 00179 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00180 $ PARAMS, WORK, IWORK, INFO) 00181 ELSE IF ( LSAMEN( 2, C2, 'GB' ) ) THEN 00182 CALL DGBSVXX(FACT, TRANS, N, KL, KU, NRHS, ABCOPY, 00183 $ LDAB, AFB, LDAFB, IPIV, EQUED, R, C, B, 00184 $ LDA, X, LDA, ORCOND, RPVGRW, BERR, NERRBND, 00185 $ ERRBND_N, ERRBND_C, NPARAMS, PARAMS, WORK, IWORK, 00186 $ INFO) 00187 ELSE 00188 CALL DGESVXX(FACT, TRANS, N, NRHS, ACOPY, LDA, AF, LDA, 00189 $ IPIV, EQUED, R, C, B, LDA, X, LDA, ORCOND, 00190 $ RPVGRW, BERR, NERRBND, ERRBND_N, ERRBND_C, NPARAMS, 00191 $ PARAMS, WORK, IWORK, INFO) 00192 END IF 00193 00194 N_AUX_TESTS = N_AUX_TESTS + 1 00195 IF (ORCOND .LT. EPS) THEN 00196 ! Either factorization failed or the matrix is flagged, and 1 <= 00197 ! INFO <= N+1. We don't decide based on rcond anymore. 00198 ! IF (INFO .EQ. 0 .OR. INFO .GT. N+1) THEN 00199 ! NFAIL = NFAIL + 1 00200 ! WRITE (*, FMT=8000) N, INFO, ORCOND, RCOND 00201 ! END IF 00202 ELSE 00203 ! Either everything succeeded (INFO == 0) or some solution failed 00204 ! to converge (INFO > N+1). 00205 IF (INFO .GT. 0 .AND. INFO .LE. N+1) THEN 00206 NFAIL = NFAIL + 1 00207 WRITE (*, FMT=8000) C2, N, INFO, ORCOND, RCOND 00208 END IF 00209 END IF 00210 00211 * Calculating the difference between D**SVXX's X and the true X. 00212 DO I = 1,N 00213 DO J =1,NRHS 00214 DIFF(I,J) = X(I,J) - INVHILB(I,J) 00215 END DO 00216 END DO 00217 00218 * Calculating the RCOND 00219 RNORM = 0.0D+0 00220 RINORM = 0.0D+0 00221 IF ( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN 00222 DO I = 1, N 00223 SUMR = 0.0D+0 00224 SUMRI = 0.0D+0 00225 DO J = 1, N 00226 SUMR = SUMR + S(I) * ABS(A(I,J)) * S(J) 00227 SUMRI = SUMRI + ABS(INVHILB(I, J)) / (S(J) * S(I)) 00228 00229 END DO 00230 RNORM = MAX(RNORM,SUMR) 00231 RINORM = MAX(RINORM,SUMRI) 00232 END DO 00233 ELSE IF ( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'GB' ) ) 00234 $ THEN 00235 DO I = 1, N 00236 SUMR = 0.0D+0 00237 SUMRI = 0.0D+0 00238 DO J = 1, N 00239 SUMR = SUMR + R(I) * ABS(A(I,J)) * C(J) 00240 SUMRI = SUMRI + ABS(INVHILB(I, J)) / (R(J) * C(I)) 00241 END DO 00242 RNORM = MAX(RNORM,SUMR) 00243 RINORM = MAX(RINORM,SUMRI) 00244 END DO 00245 END IF 00246 00247 RNORM = RNORM / ABS(A(1, 1)) 00248 RCOND = 1.0D+0/(RNORM * RINORM) 00249 00250 * Calculating the R for normwise rcond. 00251 DO I = 1, N 00252 RINV(I) = 0.0D+0 00253 END DO 00254 DO J = 1, N 00255 DO I = 1, N 00256 RINV(I) = RINV(I) + ABS(A(I,J)) 00257 END DO 00258 END DO 00259 00260 * Calculating the Normwise rcond. 00261 RINORM = 0.0D+0 00262 DO I = 1, N 00263 SUMRI = 0.0D+0 00264 DO J = 1, N 00265 SUMRI = SUMRI + ABS(INVHILB(I,J) * RINV(J)) 00266 END DO 00267 RINORM = MAX(RINORM, SUMRI) 00268 END DO 00269 00270 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00271 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00272 NCOND = ABS(A(1,1)) / RINORM 00273 00274 CONDTHRESH = M * EPS 00275 ERRTHRESH = M * EPS 00276 00277 DO K = 1, NRHS 00278 NORMT = 0.0D+0 00279 NORMDIF = 0.0D+0 00280 CWISE_ERR = 0.0D+0 00281 DO I = 1, N 00282 NORMT = MAX(ABS(INVHILB(I, K)), NORMT) 00283 NORMDIF = MAX(ABS(X(I,K) - INVHILB(I,K)), NORMDIF) 00284 IF (INVHILB(I,K) .NE. 0.0D+0) THEN 00285 CWISE_ERR = MAX(ABS(X(I,K) - INVHILB(I,K)) 00286 $ /ABS(INVHILB(I,K)), CWISE_ERR) 00287 ELSE IF (X(I, K) .NE. 0.0D+0) THEN 00288 CWISE_ERR = DLAMCH('OVERFLOW') 00289 END IF 00290 END DO 00291 IF (NORMT .NE. 0.0D+0) THEN 00292 NWISE_ERR = NORMDIF / NORMT 00293 ELSE IF (NORMDIF .NE. 0.0D+0) THEN 00294 NWISE_ERR = DLAMCH('OVERFLOW') 00295 ELSE 00296 NWISE_ERR = 0.0D+0 00297 ENDIF 00298 00299 DO I = 1, N 00300 RINV(I) = 0.0D+0 00301 END DO 00302 DO J = 1, N 00303 DO I = 1, N 00304 RINV(I) = RINV(I) + ABS(A(I, J) * INVHILB(J, K)) 00305 END DO 00306 END DO 00307 RINORM = 0.0D+0 00308 DO I = 1, N 00309 SUMRI = 0.0D+0 00310 DO J = 1, N 00311 SUMRI = SUMRI 00312 $ + ABS(INVHILB(I, J) * RINV(J) / INVHILB(I, K)) 00313 END DO 00314 RINORM = MAX(RINORM, SUMRI) 00315 END DO 00316 ! invhilb is the inverse *unscaled* Hilbert matrix, so scale its norm 00317 ! by 1/A(1,1) to make the scaling match A (the scaled Hilbert matrix) 00318 CCOND = ABS(A(1,1))/RINORM 00319 00320 ! Forward error bound tests 00321 NWISE_BND = ERRBND_N(K + (BND_I-1)*NRHS) 00322 CWISE_BND = ERRBND_C(K + (BND_I-1)*NRHS) 00323 NWISE_RCOND = ERRBND_N(K + (COND_I-1)*NRHS) 00324 CWISE_RCOND = ERRBND_C(K + (COND_I-1)*NRHS) 00325 ! write (*,*) 'nwise : ', n, k, ncond, nwise_rcond, 00326 ! $ condthresh, ncond.ge.condthresh 00327 ! write (*,*) 'nwise2: ', k, nwise_bnd, nwise_err, errthresh 00328 IF (NCOND .GE. CONDTHRESH) THEN 00329 NGUAR = 'YES' 00330 IF (NWISE_BND .GT. ERRTHRESH) THEN 00331 TSTRAT(1) = 1/(2.0D+0*EPS) 00332 ELSE 00333 IF (NWISE_BND .NE. 0.0D+0) THEN 00334 TSTRAT(1) = NWISE_ERR / NWISE_BND 00335 ELSE IF (NWISE_ERR .NE. 0.0D+0) THEN 00336 TSTRAT(1) = 1/(16.0*EPS) 00337 ELSE 00338 TSTRAT(1) = 0.0D+0 00339 END IF 00340 IF (TSTRAT(1) .GT. 1.0D+0) THEN 00341 TSTRAT(1) = 1/(4.0D+0*EPS) 00342 END IF 00343 END IF 00344 ELSE 00345 NGUAR = 'NO' 00346 IF (NWISE_BND .LT. 1.0D+0) THEN 00347 TSTRAT(1) = 1/(8.0D+0*EPS) 00348 ELSE 00349 TSTRAT(1) = 1.0D+0 00350 END IF 00351 END IF 00352 ! write (*,*) 'cwise : ', n, k, ccond, cwise_rcond, 00353 ! $ condthresh, ccond.ge.condthresh 00354 ! write (*,*) 'cwise2: ', k, cwise_bnd, cwise_err, errthresh 00355 IF (CCOND .GE. CONDTHRESH) THEN 00356 CGUAR = 'YES' 00357 IF (CWISE_BND .GT. ERRTHRESH) THEN 00358 TSTRAT(2) = 1/(2.0D+0*EPS) 00359 ELSE 00360 IF (CWISE_BND .NE. 0.0D+0) THEN 00361 TSTRAT(2) = CWISE_ERR / CWISE_BND 00362 ELSE IF (CWISE_ERR .NE. 0.0D+0) THEN 00363 TSTRAT(2) = 1/(16.0D+0*EPS) 00364 ELSE 00365 TSTRAT(2) = 0.0D+0 00366 END IF 00367 IF (TSTRAT(2) .GT. 1.0D+0) TSTRAT(2) = 1/(4.0D+0*EPS) 00368 END IF 00369 ELSE 00370 CGUAR = 'NO' 00371 IF (CWISE_BND .LT. 1.0D+0) THEN 00372 TSTRAT(2) = 1/(8.0D+0*EPS) 00373 ELSE 00374 TSTRAT(2) = 1.0D+0 00375 END IF 00376 END IF 00377 00378 ! Backwards error test 00379 TSTRAT(3) = BERR(K)/EPS 00380 00381 ! Condition number tests 00382 TSTRAT(4) = RCOND / ORCOND 00383 IF (RCOND .GE. CONDTHRESH .AND. TSTRAT(4) .LT. 1.0D+0) 00384 $ TSTRAT(4) = 1.0D+0 / TSTRAT(4) 00385 00386 TSTRAT(5) = NCOND / NWISE_RCOND 00387 IF (NCOND .GE. CONDTHRESH .AND. TSTRAT(5) .LT. 1.0D+0) 00388 $ TSTRAT(5) = 1.0D+0 / TSTRAT(5) 00389 00390 TSTRAT(6) = CCOND / NWISE_RCOND 00391 IF (CCOND .GE. CONDTHRESH .AND. TSTRAT(6) .LT. 1.0D+0) 00392 $ TSTRAT(6) = 1.0D+0 / TSTRAT(6) 00393 00394 DO I = 1, NTESTS 00395 IF (TSTRAT(I) .GT. THRESH) THEN 00396 IF (.NOT.PRINTED_GUIDE) THEN 00397 WRITE(*,*) 00398 WRITE( *, 9996) 1 00399 WRITE( *, 9995) 2 00400 WRITE( *, 9994) 3 00401 WRITE( *, 9993) 4 00402 WRITE( *, 9992) 5 00403 WRITE( *, 9991) 6 00404 WRITE( *, 9990) 7 00405 WRITE( *, 9989) 8 00406 WRITE(*,*) 00407 PRINTED_GUIDE = .TRUE. 00408 END IF 00409 WRITE( *, 9999) C2, N, K, NGUAR, CGUAR, I, TSTRAT(I) 00410 NFAIL = NFAIL + 1 00411 END IF 00412 END DO 00413 END DO 00414 00415 c$$$ WRITE(*,*) 00416 c$$$ WRITE(*,*) 'Normwise Error Bounds' 00417 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,nwise_i,bnd_i) 00418 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,nwise_i,cond_i) 00419 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,nwise_i,rawbnd_i) 00420 c$$$ WRITE(*,*) 00421 c$$$ WRITE(*,*) 'Componentwise Error Bounds' 00422 c$$$ WRITE(*,*) 'Guaranteed error bound: ',ERRBND(NRHS,cwise_i,bnd_i) 00423 c$$$ WRITE(*,*) 'Reciprocal condition number: ',ERRBND(NRHS,cwise_i,cond_i) 00424 c$$$ WRITE(*,*) 'Raw error estimate: ',ERRBND(NRHS,cwise_i,rawbnd_i) 00425 c$$$ print *, 'Info: ', info 00426 c$$$ WRITE(*,*) 00427 * WRITE(*,*) 'TSTRAT: ',TSTRAT 00428 00429 END DO 00430 00431 WRITE(*,*) 00432 IF( NFAIL .GT. 0 ) THEN 00433 WRITE(*,9998) C2, NFAIL, NTESTS*N+N_AUX_TESTS 00434 ELSE 00435 WRITE(*,9997) C2 00436 END IF 00437 9999 FORMAT( ' D', A2, 'SVXX: N =', I2, ', RHS = ', I2, 00438 $ ', NWISE GUAR. = ', A, ', CWISE GUAR. = ', A, 00439 $ ' test(',I1,') =', G12.5 ) 00440 9998 FORMAT( ' D', A2, 'SVXX: ', I6, ' out of ', I6, 00441 $ ' tests failed to pass the threshold' ) 00442 9997 FORMAT( ' D', A2, 'SVXX passed the tests of error bounds' ) 00443 * Test ratios. 00444 9996 FORMAT( 3X, I2, ': Normwise guaranteed forward error', / 5X, 00445 $ 'Guaranteed case: if norm ( abs( Xc - Xt )', 00446 $ ' / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ), then', 00447 $ / 5X, 00448 $ 'ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS') 00449 9995 FORMAT( 3X, I2, ': Componentwise guaranteed forward error' ) 00450 9994 FORMAT( 3X, I2, ': Backwards error' ) 00451 9993 FORMAT( 3X, I2, ': Reciprocal condition number' ) 00452 9992 FORMAT( 3X, I2, ': Reciprocal normwise condition number' ) 00453 9991 FORMAT( 3X, I2, ': Raw normwise error estimate' ) 00454 9990 FORMAT( 3X, I2, ': Reciprocal componentwise condition number' ) 00455 9989 FORMAT( 3X, I2, ': Raw componentwise error estimate' ) 00456 00457 8000 FORMAT( ' D', A2, 'SVXX: N =', I2, ', INFO = ', I3, 00458 $ ', ORCOND = ', G12.5, ', real RCOND = ', G12.5 ) 00459 00460 END
1.7.3 
